Juan had $5.25 in nickels and quarters. if he had 15 more nickels than quarters, how many quarters did he have?

We will need to have a model for this problem to easily solve it.

First, let us say x is the number of nickels Juan had, and y is the number of quarters Juan had.

Now, we all know that a nickel is worth 5 cents and a quarter is worth 25 cents. The given said Juan had a total amount of nickels and quarters equal to $5.25 and that there should be 15 more nickels than quarters - we need a second model: $5.25 = $0.05x+$0.25y, but x = y+15 = > $5.25 = $0.05 (y+15) + $0.25y. Simplifying, we have $5.25 = $0.05y+$0.25y+$0.75 or $0.3y+$0.75.

Isolating the unknown, we have $5.25-$0.75 = $0.3y, or $4.50 = $0.3y.

Divide both sides by $0.3, we have y = 15. Therefore, x = 15+15 or 30.

Check the solution, 30 ($0.05) + 15 ($0.25) = $5.25.

Therefore, Juan had 15 quarters.